How to cut at the same height
Try the Knife tool, set your view to an ortho side view hit "K" for knife than "Z"(cut through) and "C"(constrain) than draw your edge cut.

EDIT:
Another option could be to select these edges and just right click and select subdivide and than slide that edge by double tapping "G" to move it into position. Creating edge loop cuts is usually easier when you don't have Tris though.